## volume of an ellipsoid

Well, I have a small problem. I know the general formula for the volume of an ellipsoid. But I have a task to find it with the help of an integral. Can you explain me how to do this?
 Recognitions: Homework Help We've covered this before. http://www.physicsforums.com/showthr...lume+ellipsoid And for the more special and simple case of a spheroid : http://www.physicsforums.com/showthr...ght=revolution
 Thank you very much, the information is great. And can you write the formula like in that post but for an ellipsoid where a, b and c are different.

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## volume of an ellipsoid

As Curious3141 already posted, in the link below, HallsofIvy explains it very well. What part do you not understand?

http://www.physicsforums.com/showthr...lume+ellipsoid

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 Quote by -=nobody=- Thank you very much, the information is great. And can you write the formula like in that post but for an ellipsoid where a, b and c are different.
No, that's for a spheroid (two axes equal). For the general ellipsoid use the triple integral method. Of course the final answer comes out to a simple $$V = \frac{4}{3}\pi abc$$, it's just the derivation that's involved.
 And can you please show me how we can receive this $$V = \frac{4}{3}\pi abc$$ from this $$2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx$$ And can we also use this method?